Simplify the following expression: $ a = \dfrac{t - 10}{-6t} - \dfrac{-7}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{t - 10}{-6t} \times \dfrac{3}{3} = \dfrac{3t - 30}{-18t} $ Multiply the second expression by $\dfrac{-6t}{-6t}$ $ \dfrac{-7}{3} \times \dfrac{-6t}{-6t} = \dfrac{42t}{-18t} $ Therefore $ a = \dfrac{3t - 30}{-18t} - \dfrac{42t}{-18t} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{3t - 30 - 42t }{-18t} $ Distribute the negative sign: $a = \dfrac{3t - 30 - 42t}{-18t}$ $a = \dfrac{-39t - 30}{-18t}$ Simplify the expression by dividing the numerator and denominator by -3: $a = \dfrac{13t + 10}{6t}$